English

Twisted index theory on good orbifolds, I: noncommutative Bloch theory

Differential Geometry 2007-05-23 v1 Mathematical Physics K-Theory and Homology math.MP Operator Algebras

Abstract

This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related to generalizations of the Bethe-Sommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.

Keywords

Cite

@article{arxiv.math/9911102,
  title  = {Twisted index theory on good orbifolds, I: noncommutative Bloch theory},
  author = {Matilde Marcolli and Varghese Mathai},
  journal= {arXiv preprint arXiv:math/9911102},
  year   = {2007}
}

Comments

34 pages, LaTex